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MMLU-Pro / 9557 / A uniformly solid sphere of mass M and radius R is fixed a distance h…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

A uniformly solid sphere of mass MM and radius RR is fixed a distance hh above a thin infinite sheet of mass density ρ5\rho_5 (mass/area). With what force does the sphere attract the sheet?
Plain-text mathematical notation (without MathML)
A uniformly solid sphere of mass M and radius R is fixed a distance h above a thin infinite sheet of mass density ρ₅ (mass/area). With what force does the sphere attract the sheet?
Original LaTeX notation
A uniformly solid sphere of mass $M$ and radius $R$ is fixed a distance $h$ above a thin infinite sheet of mass density $\rho_5$ (mass/area). With what force does the sphere attract the sheet?

category

physics

options

  1. $4\pi$ $\rho_s G M$
  2. $4\pi \rho_s G M/h$
  3. $3\pi$ $\rho_s G M$
  4. $8\pi \rho_s G M R^2/h$
  5. $2\pi$ $\rho_s G M$
  6. $6\pi \rho_s G M R$
  7. $\pi$ $\rho_s G M$
  8. $2\pi^2 \rho_s G M R$
  9. $2\pi \rho_s G M R/h$
  10. $5\pi \rho_s G M/h^2$

src

scibench-class

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Source and history

upstream_id / Original problem ID
9557
task_id
5d50e0ea-086a-57c9-b7fa-b438a27d2a7e
task_key
default--test--9557
task_revision_id
1
config / split
default / test

Official source

initial import